A less restrictive assumption is that we have access to proxy variables, which contain relevant side information on the confounder. In the flight tickets example, we can use the number of views of the ticket reservation page as a proxy variable, which reflects peoples' desire for flights. Note that if we can completely recover the confounder from proxy variables, the ignorable treatment assignment assumption can be satisfied based on it. Motivated by this, [1]} and [2]} aim to recover the distribution of confounders from proxy variables using modern machine learning techniques such as generative adversarial networks [3]} or variational auto-encoders (VAE) [4]}. Although these methods exhibit powerful empirical performance, there is little theory that guarantees the correct recovery of the causal effects.
